There are several common ways that authors have FTL work, they all have disadvantages and advantages. As always the limitations such drives have are just as important as their strengths, if not more so.

The first is the jump drive. This allows a ship to teleport itself, not passing through the space between at all.
In the Foundation series this is how FTL works, it is limited only by star charts and how fast the pilot/computer can do the math for the next jump.
In some books that use this system the points in space that can be jump from are the limitation.
In order for this drive to not just bulldoze all your plot away you do need to use limits to your using this one.

The second is hyperspace. This means the ship travels though a different dimension, bypassing the laws of physics by going someplace the speed of light is not a limitation.
Babylon five used this method, the ships would enter hyperspace then travel using their normal drives. Then exit when they got to the point in hyperspace that corresponded to the point in normal space they wanted to be.

The third is the warp drive. This drive allows travel faster then light through our universe. This normally involves warping or creating space. Unlike the others this one can allow tracking and interception by people not traveling FTL.

All three of these have been used effectively, and it’s quite rare to find an author who uses a method that does not fall under one of those three above.
However what is more important is what limitations the drives have. In Dark Matter the blink drive can go anywhere in one jump. In the foundation series it could take days to do the math for a single jump and that jump can only take the ship so far.

I would spend more time trying to come up with interesting limitations for one of the three above then trying to think of a new way to travel faster then light. If you can come up with one, awesome use it. But don’t beat yourself up over not being able to come up with a whole new system.

While it will not be needed for every plot line knowing what makes good science is something you should know. And just as important is knowing how to make bad science.
For example if your writing about Jor-Ell and the fall of Krypton you want him to sound like he knows what he is doing, and the mainstream scientists to sound wrong. You don’t want him to sound like a crazy who does not know what he is talking about.

The first thing to understand is that good science is open and freely available. By this I mean that the data the scientists used is freely available for review, as are the papers and such. They should want people to point out what they did wrong, if anything.
For bad science you can have some of the data set’s be secret, maybe classified or patented.

Good science is also repeatable, some would say this is the very definition of science in the first place. If you wanted to have bad science being believed one way would be to make the experiment hard to repeat, it costs too much money, it took a lot of time ect.

Lastly good science is unbiased, by this I mean that the scientists do not allow anything but logic and data sway their views. However they are as human as anyone else.
Things like political opinions can effect their views. Or it could be that if they come to the wrong conclusion they lose their job. If they built a carrier around saying the planet is stable, and mining can continue, they will hardly be the first to say it should stop.

One problem you see more often then not in any science fiction with a lot of alien races is that all members of a race can be described in the same way.
For example “Klingons are warriors” then show literally all Klingons as warriors. The thing is that can’t be true, for any number of reasons.

A large part of why this is done is practical, even with a novel to work with you would be hard pressed to describe even passingly every society on earth.
That said, you should not just throw up your hands and give up, there are things that can be done. The first is to establish that there are exceptions. Show a Klingon shop keeper, or describe a store that would not exist if the only people who were in town were warriors. If half of all Klingons are warriors then that should have great effects on their culture and society but it can’t be the only thing they are. In the least you can show occasional exceptions to the rule.

Just a little time and effort can make a race go from “The warrior race” to something more, and it gives you something to build from. If you established who Klingons are, then you meet a renowned Klingon scientists you suddenly have an interesting hook for a character. Half the reason to use stereotypes is to defy them after all.